Rigid objects in higher cluster categories
Rigid objects in higher cluster categories
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DOI：
10.1016/j.jalgebra.2008.11.007
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发表时间：
2007-12
影响因子：
0.9
通讯作者：
Anette Wrålsen
中科院分区：
文献类型：
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作者：
Anette Wrålsen
研究了具有n个非同构简单模的有限维遗传代数H的m簇范畴中的极大m刚体。我们证明了在这些范畴中所有极大的m刚体都有恰好n个非同构不可分解和，并且在chma中任何几乎完全的m刚体都有恰好m+1个非同构补。我们还证明了这些类别中的最大m-刚性对象和m-簇倾斜对象是重合的，并且证明了与最大m-刚性对象相关的有限维代数类在某些因子代数下是封闭的。
We study maximal m-rigid objects in the m-cluster category CHmassociated with a finite dimensional hereditary algebra H with n nonisomorphic simple modules. We show that all maximal m-rigid objects in these categories have exactly n nonisomorphic indecomposable summands, and that any almost complete m-rigid object in CHmhas exactly m+1 nonisomorphic complements. We also show that the maximal m-rigid objects and the m-cluster tilting objects in these categories coincide, and that the class of finite dimensional algebras associated with maximal m-rigid objects is closed under certain factor algebras.